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We realized a laboratory experiment to study the scattering polarization of the Na I D-doublet at 589.0 and 589.6 nm in the presence of a magnetic field. This work was stimulated by solar observations of that doublet, which have proven particularly challenging to explain through available models of polarized line formation, even to the point of casting doubts on our very understanding of the underlying physics. The purpose of the experiment was to test a quantum theory for the polarized scattering of spectrally flat incident radiation, on which much of the current magnetic diagnostics of stellar atmospheres is based. The experiment has confirmed the predictions of that theory, and its adequacy for the modeling of scattering polarization under flat-spectrum illumination., Comment: 5 pages, 2 figures

We present a generalized frequency redistribution function for the polarized two-term atom in an arbitrary magnetic field. This result is derived within a new formulation of the quantum problem of coherent scattering of polarized radiation by atoms in the collisionless regime. The general theory, which is based on a diagrammatic treatment of the atom-photon interaction, is still work in progress. However, the results anticipated here are relevant enough for the study of the magnetism of the solar chromosphere and of interest for astrophysics in general., Comment: ApJ, in press

Within the framework of the density matrix theory for the generation and transfer of polarized radiation, velocity density matrix correlations represent an important physical aspect that, however, is often neglected in practical applications by adopting the simplifying approximation of complete redistribution on velocity. In this paper, we present an application of the Non-LTE problem for polarized radiation taking such correlations into account through the velocity-space density matrix formalism. We consider a two-level atom with infinitely sharp upper and lower levels, and we derive the corresponding statistical equilibrium equations neglecting the contribution of velocity-changing collisions. Coupling such equations with the radiative transfer equations for polarized radiation, we derive a set of coupled equations for the velocity-dependent source function. This set of equations is then particularized to the case of a plane-parallel atmosphere. The equations presented in this paper provide a complete and solid description of the physics of pure Doppler redistribution, a phenomenon generally described within the framework of the redistribution matrix formalism. The redistribution matrix corresponding to this problem (generally referred to as R_I) is derived starting from the statistical equilibrium equations for the velocity-space density matrix and from the radiative transfer equations for polarized radiation, thus showing the equivalence of the two approaches., Comment: Accepted for publication in Astronomy & Astrophysics

The spectral line polarization of the radiation emerging from a magnetized astrophysical plasma depends on the state of the atoms within the medium, whose determination requires considering the interactions between the atoms and the magnetic field, between the atoms and photons (radiative transitions), and between the atoms and other material particles (collisional transitions). In applications within the framework of the multiterm model atom (which accounts for quantum interference between magnetic sublevels pertaining either to the same J-level or to different J-levels within the same term) collisional processes are generally neglected when solving the master equation for the atomic density matrix. This is partly due to the lack of experimental data and/or of approximate theoretical expressions for calculating the collisional transfer and relaxation rates (in particular the rates for interference between sublevels pertaining to different J-levels, and the depolarizing rates due to elastic collisions). In this paper we formally define and investigate the transfer and relaxation rates due to isotropic inelastic and superelastic collisions that enter the statistical equilibrium equations of a multiterm atom. Under the hypothesis that the atom-collider interaction can be described by a dipolar operator, we provide expressions that relate the collisional rates for interference between different J-levels to the usual collisional rates for J-level populations. Finally, we apply the general equations to the case of a two-term atom with unpolarized lower term, illustrating the impact of inelastic and superelastic collisions on scattering polarization through radiative transfer calculations in a slab of stellar atmospheric plasma anisotropically illuminated by the photospheric radiation field., Comment: Accepted for publication in Astronomy & Astrophysics

The magnetic field plays a pivotal role in many fields of Astrophysics. This is especially true for the physics of the solar atmosphere. Measuring the magnetic field in the upper solar atmosphere is crucial to understand the nature of the underlying physical processes that drive the violent dynamics of the solar corona -- that can also affect life on Earth. SolmeX, a fully equipped solar space observatory for remote-sensing observations, will provide the first comprehensive measurements of the strength and direction of the magnetic field in the upper solar atmosphere. The mission consists of two spacecraft, one carrying the instruments, and another one in formation flight at a distance of about 200m carrying the occulter to provide an artificial total solar eclipse. This will ensure high-quality coronagraphic observations above the solar limb. Solmex integrates two spectro-polarimetric coronagraphs for off-limb observations, one in the EUV and one in the IR, and three instruments for observations on the disk. The latter comprises one imaging polarimeter in the EUV for coronal studies, a spectro-polarimeter in the EUV to investigate the low corona, and an imaging spectro-polarimeter in the UV for chromospheric studies. SOHO and other existing missions have investigated the emission of the upper atmosphere in detail (not considering polarization), and as this will be the case also for missions planned for the near future. Therefore it is timely that SolmeX provides the final piece of the observational quest by measuring the magnetic field in the upper atmosphere through polarimetric observations., Comment: Submitted to Experimental Astronomy. 30 pages, 19 figures

This paper presents a detailed study of the scattering polarization profiles formed under partial frequency redistribution (PRD) in two thermal models of the solar atmosphere. Particular attention is given to understanding the influence of several atmospheric parameters on the emergent fractional linear polarization profiles. The shapes of these $Q/I$ profiles are interpreted in terms of the anisotropy of the radiation field, which in turn depends on the source function gradient that sets the angular variation of the specific intensity. We define a suitable frequency integrated anisotropy factor for PRD that can be directly related to the emergent linear polarization. We show that complete frequency redistribution is a good approximation to model weak resonance lines. We also show that the emergent linear polarization profiles can be very sensitive to the thermal structure of the solar atmosphere and, in particular, to spatial variations of the damping parameter., Comment: 45 pages, 16 figures, accepted for publication in the Astrophysical Journal (2010)

We show a selection of high-sensitivity spectropolarimetric observations obtained over the last few years in the Ba II D2-line with the Zurich Imaging Polarimeter (ZIMPOL) attached to the Gregory Coude Telescope of IRSOL. The measurements were collected close to the solar limb, in several regions with varying degree of magnetic activity. The Stokes profiles we have observed show clear signatures of the joint action of the Hanle and Zeeman effects, in very good qualitative agreement with the theoretical expectations. Polarimetric measurements of this line show to be very well suited for magnetic field diagnostics of the lower solar chromosphere, from regions with field intensities as low as 1 gauss to strongly magnetized ones having kG field strengths., Comment: 6 pages, 6 figures, presented at Solar Polarization Workshop 5, held in Ascona, Switzerland, 17-21 September 2007

A big challenge in solar and stellar physics in the coming years will be to decipher the magnetism of the solar outer atmosphere (chromosphere and corona) along with its dynamic coupling with the magnetic fields of the underlying photosphere. To this end, it is important to develop rigorous diagnostic tools for the physical interpretation of spectropolarimetric observations in suitably chosen spectral lines. Here we present a computer program for the synthesis and inversion of Stokes profiles caused by the joint action of atomic level polarization and the Hanle and Zeeman effects in some spectral lines of diagnostic interest, such as those of the He I 10830 A and D_3 multiplets. It is based on the quantum theory of spectral line polarization, which takes into account all the relevant physical mechanisms and ingredients (optical pumping, atomic level polarization, Zeeman, Paschen-Back and Hanle effects). The influence of radiative transfer on the emergent spectral line radiation is taken into account through a suitable slab model. The user can either calculate the emergent intensity and polarization for any given magnetic field vector or infer the dynamical and magnetic properties from the observed Stokes profiles via an efficient inversion algorithm based on global optimization methods. The reliability of the forward modeling and inversion code presented here is demonstrated through several applications, which range from the inference of the magnetic field vector in solar active regions to determining whether or not it is canopy-like in quiet chromospheric regions. This user-friendly diagnostic tool called "HAZEL" (from HAnle and ZEeman Light) is offered to the astrophysical community, with the hope that it will facilitate new advances in solar and stellar physics., Comment: 62 pages, 19 figures, 3 tables. Accepted for publication in ApJ

We present first results of a systematic investigation of the incomplete Paschen-Back effect in magnetic Ap stars. A short overview of the theory is followed by a demonstration of how level splittings and component strengths change with magnetic field strength for some lines of special astrophysical interest. Requirements are set out for a code which allows the calculation of full Stokes spectra in the Paschen-Back regime and the behaviour of Stokes I and V profiles of transitions in the multiplet 74 of FeII is discussed in some detail. It is shown that the incomplete Paschen-Back effect can lead to noticeable line shifts which strongly depend on total multiplet strength, magnetic field strength and field direction. Ghost components (which violate the normal selection rule on J) show up in strong magnetic fields but are probably unobservable. Finally it is shown that measurements of the integrated magnetic field modulus $H_s$ are not adversely affected by the Paschen-Back effect, and that there is a potential problem in (magnetic) Doppler mapping if lines in the Paschen-Back regime are treated in the Zeeman approximation., Comment: 8 pages, 10 figures, to appear in MNRAS

The Zeeman pattern of MnI lines is sensitive to hyperfine structure (HFS) and, they respond to hG magnetic field strengths differently from the lines used in solar magnetometry. This peculiarity has been employed to measure magnetic field strengths in quiet Sun regions. However, the methods applied so far assume the magnetic field to be constant in the resolution element. The assumption is clearly insufficient to describe the complex quiet Sun magnetic fields, biasing the results of the measurements. We present the first syntheses of MnI lines in realistic quiet Sun model atmospheres. The syntheses show how the MnI lines weaken with increasing field strength. In particular, kG magnetic concentrations produce NnI 5538 circular polarization signals (Stokes V) which can be up to two orders of magnitude smaller than the weak magnetic field approximation prediction. Consequently, (1) the polarization emerging from an atmosphere having weak and strong fields is biased towards the weak fields, and (2) HFS features characteristic of weak fields show up even when the magnetic flux and energy are dominated by kG fields. For the HFS feature of MnI 5538 to disappear the filling factor of kG fields has to be larger than the filling factor of sub-kG fields. Stokes V depends on magnetic field inclination according to the simple consine law. Atmospheres with unresolved velocities produce asymmetric line profiles, which cannot be reproduced by simple one-component model atmospheres. The uncertainty of the HFS constants do not limit the use of MnI lines for magnetometry., Comment: Accepted for publication in ApJ. 10 pages, 14 figures

We present the analysis of the observations of standard stars for linear polarization obtained from 1999 to 2005 within the context of the calibration plan of the FORS1 instrument of the ESO VLT. We have considered observations carried out both in imaging polarimetric and in spectropolarimetric mode. Broadband polarization was obtained in the Bessel BVRI filters; spectropolarimetry was obtained with various grisms covering different optical ranges and with a typical resolution of a few hundreds. Spectropolarimetric data have been convolved with the transmission functions of the Bessel filters, which enabled us to calculate polarization values equivalent to broadband polarization measurements in imaging mode. Finally, for each star, instrument mode, and for each Bessel filter band, we have calculated an average polarization value obtained after filtering all available data with a k-sigma clipping algorithm., Comment: to be published in: "The Future of Photometric, Spectrophotometric, and Polarimetric Standardization", ASP Conference Series, C. Sterken (ed.)

The use of polarimetric techniques is nowadays widespread among solar and stellar astronomers. However, notwithstanding the recommandations that have often been made about the publication of polarimetric results in the astronomical literature, we are still far from having a standard protocol on which to conform. In this paper we review the basic definitions and the physical significance of the Stokes parameters, and we propose a standardization of the measurement of polarized radiation., Comment: to be published in: "The Future of Photometric, Spectrophotometric, and Polarimetric Standardization", ASP Conference Series, C. Sterken (ed.)

This is a theoretical investigation on the formation of the linearly polarized line spectrum of ionized cerium in the sun. We calculate the scattering line polarization pattern emergent from a plane-parallel layer of Ce {\sc ii} atoms illuminated from below by the photospheric radiation field, taking into account the differential pumping induced in the various magnetic sublevels by the anisotropic radiation field. We find that the line polarization pattern calculated with this simple model is in good qualitative agreement with reported observations. Interestingly, the agreement improves when some amount of atomic level depolarization is considered. We find that the best fit to the observations corresponds to the situation where the ground and metastable levels are depolarized to about one fifth of the corresponding value obtained in the absence of any depolarizing mechanism. One possibility to have this situation is that the depolarizing rate value of elastic collisions is exactly $D=10^6{\rm s}^{-1}$, which is rather unlikely. Therefore, we interpret that fact as} due to the presence of a turbulent magnetic field in the limit of saturated Hanle effect for the lower-levels. For this turbulent magnetic field we obtain a lower limit of 0.8 gauss and an upper limit of 200-300 gauss., Comment: 5 pages, 2 figures, to appear in Astron. Astrophys

The \ion{He}{1} multiplet at 10830 \AA is formed in the incomplete Paschen-Back regime for typical conditions found in solar and stellar atmospheres. The positions and strengths of the various components that form the Zeeman structure of this multiplet in the Paschen-Back regime are approximated here by polynomials. The fitting errors are smaller than $\sim10^{-2}$ m\AA in the component positions and $\sim10^{-3}$ in the relative strengths. The approximant polynomials allow for a very fast implementation of the incomplete Paschen-Back regime in numerical codes for the synthesis and inversion of polarization profiles in this important multiplet., Comment: ApJ Supplements (in press)

The theory of the generation and transfer of polarized radiation, mainly developed for interpreting solar spectropolarimetric observations, allows to reconsider, in a more rigorous and elegant way, a physical mechanism that has been suggested some years ago to interpret the high degree of polarization often observed in astronomical masers. This mechanism, for which the name of 'dichroic maser' is proposed, can operate when a low density molecular cloud is illuminated by an anisotropic source of radiation (like for instance a nearby star). Here we investigate completely unsaturated masers and show that selective stimulated emission processes are capable of producing highly polarized maser radiation in a non-magnetic environment. The polarization of the maser radiation is linear and is directed tangentially to a ring equidistant to the central star. We show that the Hanle effect due to the presence of a magnetic field can produce a rotation (from the tangential direction) of the polarization by more that 45 degrees for some selected combinations of the strength, inclination and azimuth of the magnetic field vector. However, these very same conditions produce a drastic inhibition of the maser effect. The rotations of about 90 degrees observed in SiO masers in the evolved stars TX Cam by Kemball & Diamond (1997) and IRC+10011 by Desmurs et al (2000) may then be explainedby a local modification of the anisotropy of the radiation field, being transformed from mainly radial to mainly tangential., Comment: Accepted for publication on ApJ

An attractive diagnostic tool for investigating the magnetism of the solar chromosphere is the observation and theoretical modeling of the Hanle and Zeeman effects in spicules, as shown in this letter for the first time. Here we report on spectropolarimetric observations of solar chromospheric spicules in the He I 10830 \AA multiplet and on their theoretical modeling accounting for radiative transfer effects. We find that the magnetic field in the observed (quiet Sun) spicular material at a height of about 2000 km above the visible solar surface has a strength of the order of 10 G and is inclined by approximately $35^{\circ}$ with respect to the local vertical direction. Our empirical finding based on full Stokes-vector spectropolarimetry should be taken into account in future magnetohydrodynamical simulations of spicules., Comment: 12 pages and 2 figures

We investigate the formation of polarization profiles induced by a magnetic field in the He I multiplet at 1083,0 nm . Our analysis considers the Zeeman splitting in the incomplete Paschen-Back regime. The effects turn out to be important and produce measurable signatures on the profiles, even for fields significantly weaker than the level-crossing field ($\sim$400 G). When compared to profiles calculated with the usual linear Zeeman effect, the incomplete Paschen-Back profiles exhibit the following conspicuous differences: a) a non-Doppler blueshift of the Stokes V zero-crossing wavelength of the blue component; b) area and peak asymmetries, even in the absence of velocity and magnetic gradients; c) a $\sim$25% reduction in the amplitude of the red component. These features do not vanish in the weak field limit. The spectral signatures that we analyze in this paper may be found in previous observations published in the literature., Comment: Accepted for publication in The Astrophysical Journal

We report on the a5F-y5F* multiplet of Ti I and its interest for the study of 'turbulent' magnetic fields in the quiet solar photosphere. In particular, we argue that the sizable scattering polarization signal of the 4536 \AA line (whose lower and upper levels have Land\'e factors equal to zero), relative to the rest of the lines in the multiplet, gives direct evidence for the existence of an ubiquitous, unresolved magnetic field. We cannot determine precisely the strength of the magnetic field, but its very existence is evidenced by the differential Hanle effect technique that this Ti I multiplet provides., Comment: to be published in ApJL

In a recent letter (Trujillo Bueno et al. 2002), we showed the remarkable result that the atomic alignment of the levels P$_{1/2}$ and S$_{1/2}$ of the D$_1$ line of Na I is practically destroyed in the presence of magnetic fields sensibly larger than 10 G, irrespectively of the field direction. In this paper, we demonstrate analytically that this property is a consequence of the decoupling of the electronic and nuclear angular momenta, J and I, in the excited state P$_{3/2}$, which is achieved when the Zeeman splitting from the local magnetic field becomes much larger than the typical hyperfine separation for that level., Comment: The Astrophysical Journal; 2002; in press

Magnetic fields play a key role in most astrophysical systems, from the Sun to active galactic nuclei. They can be studied through their effects on atomic energy levels, which produce polarized spectral lines. In particular, anisotropic radiation pumping processes (which send electrons to higher atomic levels) induce population imbalances that are modified by weak magnetic fields. Here we report peculiarly polarized light in the He I 10830-\AA multiplet observed in a coronal filament located at the centre of the solar disk. We show that the polarized light arises from selective absorption from the ground level of the triplet system of helium, and that it implies the presence of magnetic fields of the order of a few gauss that are highly inclined with respect to the solar radius vector. This disproves the common belief that population imbalances in long-lived atomic levels are insignificant in the presence of inclined fields with strengths in the gauss range, and demonstrates the operation of the ground-level Hanle effect in an astrophysical plasma., Comment: 22 pages and 4 figures